Global Energy Consumption Rates: Where is the Limit?

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However, there are several signals indicating in favor that the energy consumption strategy should be assumed in the near future. One signal comes from the fact that the organic fuel supplies (oil and gas) are exhausted and will come to the end in a few tens of years, and even the coal reserves will run out faster than many believe ^{[1, 2]}. The second signal comes from the fact that the global climate is now sensitive to the increasing level of energy consumption and carbon dioxide production as a result of such kind of activity, respectively. As a result, more and more discussions appear in the literature concerning whether the decrease in overall energy demand should be achieved despite a growth in both population and volume of energy services ^{[1, 3, 4, 5, 6]}, or the causal relationship between GDP and energy consumption will further persist ^{[7, 8, 9]}.

Figure 2. Comparison of the energy consumption and population growth rates in different regions of the world, derived from the International Atomic Energy Agency data

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Figure 3. Comparison of the energy consumption and population growth in (a) industrial and (b) developing countries. Calculated from data given in ref.

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Figure 4. Energy per capita for the different groups of countries as a function of time. The difference in the growth tendency for the industrial and developing countries is reflected via the slope values (tg ф) of these lines. Calculated from data given in ref.

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In this paper, the principles of the global energy consumption rates are considered from the viewpoint of thermodynamic balance between the Earth and the cosmic environment, which is necessary to maintain stable and unchanged conditions for proper functioning of the Earth biosphere. This viewpoint leads to the following principles: (i) The energy should be consumed from the renewable sources only; (ii) The amount of the consumed energy should not exceed the natural production of energy due to incoming solar radiation which gives rise to formation of organic fuel, etc. Sun is considered as a global supplier of the renewable energy on the Earth, leading to formation of all sources of the organic fuel through photosynthesis, as well as energy of wind, hydro-energy through local heating of the earth surface, melting of ice, etc. Nuclear energy is not included in this balance since nuclear materials are not renewable and, moreover, nuclear waste still represents a very dangerous factor for the biosphere.

Among various transformations of solar energy which can be consumed, there are three major energy fluxes to be considered, namely, a direct solar irradiation, an indirect solar energy through products of photosynthesis and, finally, a reemitted energy from the Earth after the heating of the planet and its re-emission as a black body radiation at the heated temperature. As to the first flux, it is considered that although the power of incoming solar irradiation at the earth surface is of the order of 10¹⁷W, only a small part of that, approximately 10¹⁴W, can be utilized by solar cells due to limitations in their efficiency, as well as limitation in the earth area suitable for their displacement. The second way of using the energy through products of photosynthesis can also yield a maximum consumption rate of 10¹⁴W which is equivalent to the energy power production by the biosphere. The total rate of human energy consumption is of the order of 10¹³W at the moment ^[10]. With the average 1.5% annual increase of the energy consumption on the Earth it will take about 150 years to reach the maximal possible limit of 10¹⁴W. Finally, there is a large domain of the renewable energy resource in the form of the outgoing terrestrial radiation which could yield additional income and shift the above limit of consumption to higher values. The methods to develop this domain will be discussed below. However, such a shift in energy consumption can be accompanied with unpredictable changes in temperature regimes on the Earth surface. Therefore, the energy consumption limit should be postulated anyway as soon as possible in the near future.

2. Global Energy Balance on the Earth

Let us consider the Earth as a thermodynamic system, with Sun as the source of the external incoming energy and a cosmic environment as a sink for the dissipated outgoing energy. The solar radiation reaching the earth surface has an average power per square meter of about 230W/m² and its spectrum extends from the UV to the IR, where the major part of energy falls in the visible range with the maximum at the wavelength of about 0.5μm (Figure 5). Eventually, the same amount of energy must be lost by the ‘Earth-atmosphere’ system if the internal energy of this system remains constant and the climate is unchanged. Therefore, the Earth emits the terrestrial radiation as a heated body. However, the spectral range of this outgoing radiation is shifted to the IR since the average temperature of the radiative body, i.e., the Earth, is 288⁰ K (Figure 5). Although the peak amount of photons of the outgoing terrestrial radiation (which takes place at the wavelength of ca. 10 μm) is much smaller as compared to the corresponding peak of the incoming solar radiation at 0.5μm, i.e., 7x10^-3 versus 1.5x10³W/(m²μm), respectively (calculated using the data from ref. ^[12]), the outgoing radiation has a much wider spectral range, so that the total amount of outgoing energy is equal to the incoming one in accordance with the thermodynamic balance of the planet.

On the other hand, the amount of photons incoming to and outgoing from the Earth is rather different according to the balance of the incoming and outgoing energy, i.e.

where n_i is the amount of photons with the frequency ν_i, h the Planck constant. It can be roughly evaluated this relationship as N_earth/N_sun=20, where N_earth is the average number of photons with the wavelength of 10μm emitted by the ‘Earth-atmosphere’ system and N_sun is the average number of photons with the wavelength of 0.5μm from the Sun.

Figure 5. Relationship between incoming solar (blue curve) and outgoing terrestrial (red curve) radiation. The magnitude of the terrestrial radiation is magnified by a factor of 500,000

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Figure 6. Relationship between incoming, stored, and outgoing energy rates per each 1000 photons from the Sun

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However, there is a small disbalance between the incoming and outgoing energy, because a small part of photons from the Sun is stored in the form of chemical energy due to photosynthesis. This part of photons can be roughly evaluated taking into account the energy conversion efficiency of photosynthesis which is of the order of 0.1% (see section 3 for details) that results in only a single stored photon of the thousand ones that are coming from the Sun. As a result, the relationship of the incoming, stored and outgoing energies can be presented schematically in Figure 6. Since only one incoming photon of one thousand gives rise to formation of all organic minerals and fuel, such as coal, natural gas, and petroleum as the products of photosynthesis, it can be easy to understand that only a small part of the incoming solar energy is consumed by the mankind through the organic fuel reserves.

3.Renewable Sources of Energy

Figure 6 illustrates various energy sources available on the Earth. These sources consist of energy reserves, such as biomass and organic fuel, geothermal, solar and gravitation energy, nuclear reserves, whose total energy is indicated in Joules. Solar and gravitation energy produces energy fluxes, such as wind, tides, water streams, etc., whose total energy power is indicated in Watts, which can be used directly. As can be seen in Figure 6, the most energetic fluxes (~10¹⁷W) are related to solar and terrestrial radiation, followed by wind ^[13], tides, and photosynthesis (~10¹⁴W). Although the power of the last three fluxes is of the same order, only a small part of the wind’s and tide’s energy can be utilized due to their significant local instability and dissipation over the Earth. Therefore, we consider only three major energy fluxes, i.e., solar and terrestrial radiation and photosynthesis.

a. Photosynthesis

The energy flux utilized by photosynthesis, P^↓_org, is of the order of 10¹⁴ W. This value can be calculated from the photosynthesis equation, i.e.

(1)

The process described by Eq. (1) involves 4 electrons to be transferred; each of them requires the energy of 1.2eV per electron. Therefore, formation of an O₂ molecule requires consumption of 4.8eV. However, quantum efficiency of the system is low and needs on average 10 (from 8 to 12) photons of the visible light (~2eV) to be adsorbed, which results in synthesis of one molecule of oxygen. Therefore, the total energy consumed by the photosynthetic system to produce one molecule of O₂will be approximately E_O2~10 quanta x 2eV = 20eV. Green plants produce totally 10¹⁴kg of O₂ annually; this corresponds to the oxygen mass rate production m_O2=3x10⁹g per second. The energy power necessary to produce O₂, therefore, will be

(2)

where M=32 is the molar mass of O₂, N_A the Avogadro constant. Using this result and the power of solar energy reaching the Earth surface which is

where albedo is taken as 28%, one can evaluate the average efficiency of photosynthesis as

(3)

The same value for η_org can be also obtained via expression P^↓_org = η_org S_earth∙230 W/m², where an assumption is made that the plants cover the overall earth surface S_earth. In fact, this assumption is rather crude, because there are large deserts, ice or mountain areas free of plants, but which can be overcompensated, however, by plant diversity in forests which occupy a few levels of space from the earth surface. The efficiency value (3) can also vary depending on the local conditions of growth of plant organisms, reaching, for example, up to 2% for water-plants grown in special pools ^[14].

It is natural to assume that the rate of energy consumption based on products of photosynthesis (gas, oil, coal, etc.) should not exceed the rate of energy formation stored in these organic products through photosynthesis, if the concept of energy consumption refers to these resources as the basic sources of energy. Thus, the energy consumption rate should be limited to P_org< 10¹⁴ W. This value is only one order of magnitude higher than the total power of all industrial energy producers currently on the Earth (about 10¹³ W, as reported in ref. ^[15]). The contemporary rate of energy consumption by the mankind can be calculated by using the data on total mass of burning of dry fuel equivalent to 5∙10¹² kg of carbon per year. The energy of carbon burning is 3.3∙10⁷ J/kg which gives the energy power of 5∙10¹² W, which is consistent also with the annual energy consumption data of the order of 10¹⁷ W∙h reported in ref. ^[10].

Finally, the efficiency of conversion of the solar energy to some mechanical work or electricity by the indirect way through burning of the organic products of photosynthesis will be even smaller, assuming that power conversion efficiency of the burning process to the mechanical work or electricity is about 40%, and thus it yields only

(4)

Since power conversion efficiency of using a direct solar radiation is a few orders of magnitude higher, one can conclude that the products of photosynthesis, including organic fuel reserves (gas, oil and coal), are much expensive forms of the solar energy then the direct solar radiation itself.

b. Incoming solar radiation

The power of solar energy irradiating our planet is of the order of 10¹⁷W. That means that the theoretical maximum of the solar energy consumption can be of the same order, i.e., P_sc~10¹⁷W, if the power conversion efficiency of the corresponding devices approaches 100%. There are limitations, however, because power conversion efficiency of the conventional solar cells is far lower, of the order of _sc ~10%, and because these cells cannot be set over the whole surface of the Earth. For example, in order to produce energy comparable with that stored by photosynthesis, the area of the solar cells S_sc should be as much as 1% of the Earth surface S_earth, which can be calculated from the following expressions with account of power conversion efficiency of the photosynthetic process (Eq.(3)):

(5)

One percent of the earth surface is rather large but reasonable value, which should not significantly affect the biosphere and cropland areas. For comparison, the total urban area on the Earth is approximately 3.4∙10²km² now ^[16]; it covers approximately 0.07 % of the Earth surface. To cover surface larger than the urban area by approximately ten times seems to be a challenging, but achievable task. In this case, the rate of the solar energy consumption by the mankind will be of the order of P_sc~10¹⁴W. However, additional studies are needed to confirm that this value is acceptable and compatible with the life conditions on the Earth.

It is interesting to note that the accumulated amount of energy produced by solar cells from 1975 to 2010 has doubled every 2.5 years and now reached the level of almost 3·10¹⁰W ^[17]. This exponential growth formally follows the Moor’s law ^[18] and if such a tendency will continue in the future, it is easy to calculate that the conventional upper level of energy production by solar cells of 10¹⁴W will be reached in the next 30 years.

Thus, the energy production rate through a direct consumption of the solar irradiation can reach practically a value one order of magnitude higher as compared with the contemporary production rate of energy through burning of organic fuel (~10¹³W, see previous section). In addition, power conversion efficiency of the direct conversion of solar energy by a modest solar cell (η_sc ~10%) is three orders of magnitude higher as compared with that of the indirect production of energy (see Eq.(4)). Thus, a direct consumption of the solar energy is more efficient than the apparent efficiency of burning of the carbon-containing products, such as oil, gas, coal and biomass.

c. Outgoing terrestrial radiation

There is a large part of IR energy, P^↑_earth, which is reemitted from the earth surface in the form of the terrestrial radiation, because the Earth emits as the black body with the temperature of T_earth=255⁰ K. The amount of this energy is huge and comparable with that coming from the sun to the earth surface, due to the thermodynamic balance of the planet (see Figure 6),

There are several classes of materials that can be used as converters of this IR energy to electricity, such as pyroelectric and thermoelectric materials, gapless semiconductors, thermocouples, etc.; however, their proper application in respect to the terrestrial energy has not been developed yet. The advantages of the consumption of the terrestrial radiation are following. First, this radiation is highly scattered and therefore there is no need for surface orientation of the corresponding IR receivers or this orientation is not so critical as compared with the solar cells converting direct solar irradiation. Therefore, such IR receivers can occupy several levels upward from the earth surface without notable shadow effect. Second, these devices do not compete with green plants for the solar light, since they operate in the other spectral range. Below we consider three classes of materials which can be potentially used for the above energy domain.

It is well known that some semiconductors are gapless or have a narrow band gap smaller than 1eV (equivalent to ~0.8μm). Many of these semiconductor crystals have the band gap values that allow them to absorb in the near-IR range (Table 1). However, there are few candidates, i.e., HgSe, HgTe, Hg_xCd_1-xTe, which can collect energy from the middle and even far IR range also. These last compounds, however, are toxic, and their application, therefore, are to be restricted. Nevertheless, development of these materials in the form of colloidal particles ^[19] packed in the inert matrix might overcome this problem. The advantage of the nanoparticle application is also due to opportunity to tune their range of absorption by simple changes of the particle size (Figure 7).

Table 1. Some semiconductor crystals absorbing IR radiation

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Figure 7. Variation of the band gap of some semiconductor crystals controlled by the crystal size. Adapted from ref.

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Figure 8. Examples of some organic compounds absorbing in the IR: a) donor-acceptor-donor D-π-A-π-D; b) TTF-σ-TCNQ; c) TTF-dithiolato metal complexes (R=(CH2)3, M=Ni; R=S(CH2)3S, M=Ni; R=Me, M=Ni; R=H, M=Pd) followed by their absorption spectra (Adapted from ref. )

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